{"paper":{"title":"Full Characterization of embedding relations between alpha modulation spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dashan Fan, Guoping Zhao, Huoxiong Wu, Weichao Guo","submitted_at":"2016-06-04T15:29:01Z","abstract_excerpt":"In this paper, we consider the embedding relations between any two $\\alpha$% -modulation spaces. Based on an observation that the $\\alpha$-modulation space with smaller $\\alpha$ can be regarded as a corresponding $\\alpha$% -modulation space with larger $\\alpha$, we give a complete characterization of the Fourier multipliers between $\\alpha$-modulation spaces with different $\\alpha$. Then we establish a full version of optimal embedding relations between $\\alpha$-modulation spaces. As an application, we determine that the bounded operators commuting with translations between $\\alpha$-modulation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01386","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}